A new independent limit on the cosmological constantdark energy from the relativistic bending of light by Galaxies and clusters of Galaxies

We derive new limits on the value of the cosmological constant, Λ, based on the Einstein bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. We use an amended lens equation in which the contribution of Λ to the Einstein deflection angle is taken into account and use observations of Einstein radii around several lens systems. We use in our calculations a Schwarzschild–de Sitter vacuole exactly matched into a Friedmann–Robertson–Walker background and show that a Λ-contribution term appears in the deflection angle within the lens equation. We find that the contribution of the Λ-term to the bending angle is larger than the second-order term for many lens systems. Using these observations of bending angles, we derive new limits on the value of Λ. These limits constitute the best observational upper bound on Λ after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints.